{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimized Reward Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Position reward based upon approach course\n",
    "\n",
    "This reward gives a higher reward the closer the airplane gets on approach course inbound to the FAF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "\n",
    "def relative_angle(angle1, angle2):\n",
    "    return (angle2 - angle1 + 180) % 360 - 180\n",
    "\n",
    "def f_reward(x, y):    \n",
    "    to_faf_x = x_faf - x\n",
    "    to_faf_y = y_faf - y\n",
    "    d_faf = np.hypot(to_faf_x, to_faf_y)\n",
    "    \n",
    "    reward_faf = 1/np.maximum(np.power(d_faf, 0.2),1)\n",
    "    angle_faf = np.degrees(np.arctan2(to_faf_y, to_faf_x))\n",
    "    \n",
    "    reward_app_sector = np.power(np.abs(relative_angle(phi_runway, angle_faf))/180, 1.5)\n",
    "    \n",
    "    reward = reward_app_sector * reward_faf\n",
    "    \n",
    "    return reward\n",
    "\n",
    "x_faf = 20\n",
    "y_faf = 15\n",
    "\n",
    "phi_runway = 310\n",
    "x_runway = 20\n",
    "y_runway = 20\n",
    "\n",
    "x = np.arange(0, 40, 0.1)\n",
    "y = np.arange(0, 40, 0.1)\n",
    "xx, yy = np.meshgrid(x, y, sparse=True)\n",
    "z = f_reward(xx, yy)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.pcolormesh(x,y,z)\n",
    "plt.colorbar()\n",
    "ax = plt.gca()\n",
    "ax.set_aspect('equal', 'datalim')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 360, 1)\n",
    "y = np.arange(0, 360, 1)\n",
    "xx, yy = np.meshgrid(x, y, sparse=True)\n",
    "z = relative_angle(xx, yy)\n",
    "#z = np.abs(z)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.pcolormesh(x,y,z)\n",
    "plt.colorbar()\n",
    "ax = plt.gca()\n",
    "ax.set_aspect('equal', 'datalim')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "130"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_angle(90, 220)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(0, 360, 0.1)\n",
    "y = np.abs(relative_angle(20, x))/180\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reward of airplane course to runway heading\n",
    "Needs to be based upon the side of the approach course on which the aicraft resides. \n",
    "\n",
    "This can be factored in using the signum of the relative angle between the angles of the approach course and airplanes relative heading to the FAF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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q6lRVfaSqXruKBpmnZ0OZyweADXdZVZ1aWL+ju+9YWN+pHLRjb6Cq+itJTiT5Swubv6m7z1TVtyT5YFV9ort/4zANFno2nPADwF519nzraRU+190ndtl/OslVC+tXJjmz/aCqemWSH07yl7r7y+e3d/eZ4e/jVfXhJC9JcqjQ4/bWSLjlBcDIfCzJtVV1TVVdnOTmJF8xCquqXpLkHyZ5TXc/ubD9kqp65vD6siQvTfKpwzZI6BkRwQeAC+k1LRdsR/fTSd6Y5GSSR5K8t7sfrqq3VtX50Vh/L8nXJ/mn24amvzDJqap6KMmHktze3YcOPW5vjczJMw+51QXAKHT3fUnu27btRxZev3LJ+34lybetuj0qPSOk4gPAjnqjhqxvHKFnpDy6AgD2x+0tAJiSPT4iYo5UekZOxQcA9kbomQjBB4BEn57dCD0TIvgAwHJCz8QIPgDz1r2eZYyEngnSzwcAvprQM2GCD8C8dPTp2Y3QM3GCDwBsMU/PDHhSO8BMdJKRVmHWQaVnRlR9AJgzoQcAmAWhZ2ZUewCmzZD15YSeGTKkHYA5EnpmTPABmKBe0zJCQs/MCT4AzIXQg+ADMBnrmZjQ5ISMmuADwNSZnJA/thh8TGQIMFIj7W+zDio97EjlB4CpUekBgKnojLa/zTqo9LCUag8AUyL0sCvBB2BkzNOzlNDDBQk+AEyBPj3syfngY1QXwKbTp2cZlR72xXO7ABgroYcDEXwANpQ+PUsJPRyY4APAmAg9HIrgA8BY6MjMoenkDLBBRnrraR1UegCAWRB6WBm3ugCOWSfpWs8yQkIPKyX4ALCp9Olh5fTxATg+rU/PUio9HBlVHwA2iUoPR0rVB2DNVHqWUulhLVR9ADhuQg9rI/gArIHRW0sJPayV4APAcdGnBwAmpPTpWUqlh7VT7QHgOAg9HAvBB+AI9BqXEXJ7i2OzGHwMaQfgqKn0sBFUfgBWYU0jt4zegsMRfAA4SkIPG0XwAeCoCD1sHMEH4BB0ZF5K6GEjnTzzkPADwEoZvQUAUzLSKsw6qPSw0VR8AFgVoYdREHwA9kifnqWEHkZD8AHgMIQeRkXwAdhFx+SEuxB6GB39fAA4CKGH0RJ8AL5a9XqWMRJ6GDXBB4C9EnoYPcEHYIHRW0tdMPRU1VVV9aGqeqSqHq6qHxy2X1pV91fVo8PfS46+ubAz/XwAuJC9VHqeTvLfdfcLk3xnkh+oqhcleXOSD3T3tUk+MKwDACRJqurGqvp0VT1WVV+VE6rqmVX1nmH/R6vq6oV9bxm2f7qqXr2K9lww9HT3E939a8Pr30vySJIrktyU5K7hsLuSvHYVDYLDUPEB2AxVdVGSdyb57iQvSnLLUDRZ9IYkX+jufy/JO5K8fXjvi5LcnOTPJrkxyf82fN6h7KtPz5DAXpLko0me391PJFvBKMnzDtsYWBXBB5irDRq9dX2Sx7r78e7+oyR3Z6tgsmixgHJPkldUVQ3b7+7uL3f3byZ5bPi8Q9lz6Kmqr0/y80n+Rnf/7j7ed1tVnaqqU7/z+bMHaSMciOADcKyuSPKZhfXTw7Ydj+nup5P82yTP2eN7921PoaeqvjZbgefnuvsXhs2frarLh/2XJ3lyp/d29x3dfaK7Tzz3OYeuTMG+CD7A7KxvRubLzhc1huW2bS3Zadrm7TWiZcfs5b37tpfRW5XkXUke6e6/v7Dr3iS3Dq9vTfK+wzYGjoLgA3AkPne+qDEsd2zbfzrJVQvrVyY5s+yYqnpGkn8nyVN7fO++7aXS89Ik/2WSl1fVg8PyPUluT3JDVT2a5IZhHTaS4AOwdh9Lcm1VXVNVF2erY/K9245ZLKC8LskHu7uH7TcPo7uuSXJtkl89bIOecaEDuvtfZecyU5K84rANgHVZDD6vfsGLj7ElAEdkgyYO7O6nq+qNSU4muSjJnd39cFW9Ncmp7r43W3eS/nFVPZatCs/Nw3sfrqr3JvlUtqbO+YHuPnTH4AuGHpiik2ceEnwAjlh335fkvm3bfmTh9R8mef2S974tydtW2R6hBwCmZEMqPZvIs7eYLf18AOZF6GHWBB9gajZocsKNI/Qwe4IPwDzo0wP5k+CjczMweiOtwqyDSg8s8MBSgOkSemAHgg8wWr2mZYSEHlhC8AGYFqEHdiH4AGOyrpFbRm/BROnnAzANRm8BwJT0ssdlotIDe6TaAzBuQg/sg+ADbDyjt5YSemCfBB+AcRJ64AB0bgYYHx2Z4RA8vgLYNGMdTr4OKj2wAqo+AJtP6IEVEXyAjaAj81JCD6yQ4AOwufTpAYCpGPEjItZBpQdWTLUHYDOp9MARWAw+RnYBa6XSs5RKDxwxlR+AzSD0wBoIPsDaGL21lNADayL4ABwvoQfWSPABjlr1epYxEnpgzQQfgOMh9MAx8MBSgPUTegCAWRB64Bip9gArZ/TWUkIPHDO3ugDWQ+iBDSH4ABwtoQc2iOADHMqahqsbsg6shNtdAEdD6IENJfgAB6Ij81JCD2wwwQdgdYQe2HCCD7AvKj1LCT0wAvr5ABzeM467AQDAalTGO7JqHVR6YERUfAAOTuiBERJ8gKX06VlK6IGREnwA9kfogRETfICvYEbmXQk9MHKCD8DeGL0FE3A++Lz6BS8+5pYAx26kVZh1UOmBCTG6C2A5oQcmSPCBGTN6aymhBwCYBaEHJkq1B+ArCT0wYYIPzI8h68sJPTBxOjcDbBF6YCYEH5gJHZmXEnpgRgQfYM5MTggzYyJDmLARV2HWQaUHZkrVB5gboQdmTPCB6TF6azmhB2bO6C5gLvTpAYApGWkVZh1UeoAkbnUB0yf0AH9M8IHxG0Ofnqq6tKrur6pHh7+X7HDMdVX1r6vq4ar6eFX95wv7fqaqfrOqHhyW6/ZyXqEH+AqCD7AGb07yge6+NskHhvXtfj/JX+3uP5vkxiQ/UVXPXtj/t7r7umF5cC8nFXqAr6JzM4zYOGZkvinJXcPru5K89qsuo/vfdPejw+szSZ5M8tzDnFToAZYSfoAj8vzufiJJhr/P2+3gqro+ycVJfmNh89uG217vqKpn7uWkQg9wQYIPjMS6qjxblZ7LqurUwnLbYlOq6v1V9ckdlpv2c0lVdXmSf5zkr3X3uWHzW5J8a5LvSHJpkjft5bMMWQf25OSZhzy6Alj0ue4+sWxnd79y2b6q+mxVXd7dTwyh5sklx31Dkn+e5H/s7o8sfPYTw8svV9VPJ/mbe2mwSg+wZyo+wIrcm+TW4fWtSd63/YCqujjJLyb52e7+p9v2XT78rWz1B/rkXk4q9ADARNQal0O6PckNVfVokhuG9VTViar6qeGY703yF5N83w5D03+uqj6R5BNJLkvy43s5qdtbwL64zQUcVnd/Pskrdth+Ksn3D6//SZJ/suT9Lz/IeYUeYN/O3+YSfmADeQzFUm5vAQdmSDswJkIPcGiCD2yOMTyG4rgIPcBKCD7AphN6gJURfGADjOMxFMdC6AFWSj8fYFMJPcCREHzgmKj0LCX0AEdG8AE2iXl6AGAqRjyyah1UeoAjpY8PsCmEHmAtBB9YE316lhJ6gLURfIDjpE8PsFae2wVHS5+e5VR6gGOh6gOsm9ADHBvBB1gnoQc4VoIPrJiOzEsJPcCxE3yAddCRGQAmREfm5YQeYCMsVnuM7AKOgttbwMZxuwsOaF39eUZaTRJ6gI0k+ACrJvQAG0vwgQNQ6VlK6AE2muADrIqOzMDG8+gK2JuK0Vu7UekBRuPkmYdUfoADE3qA0RF8YBf69Cwl9AAAsyD0AKOk2gM7q+61LGMk9ACjJfgA+2H0FjBqRnbBghH3t1kHlR5gElR9gAsReoDJEHyA3bi9BUyK213MnckJl1PpASZJ1QfY7oKhp6rurKonq+qTC9surar7q+rR4e8lR9tMgP0zgzOzZHLCpfZS6fmZJDdu2/bmJB/o7muTfGBYB9hIgg+Q7CH0dPcvJ3lq2+abktw1vL4ryWtX3C4A4ACq17OM0UH79Dy/u59IkuHv81bXJIDVU+0Bjrwjc1XdVlWnqurU73z+7FGfDmApwYdZ0KdnqYOGns9W1eVJMvx9ctmB3X1Hd5/o7hPPfc5FBzwdwGoIPjBfBw099ya5dXh9a5L3raY5AEdP8GGy1tSfZ6x9ei44OWFVvTvJy5JcVlWnk/xoktuTvLeq3pDkt5O8/igbCbBqi8HHRIYwDxcMPd19y5Jdr1hxWwCOxckzDwk+TMdIqzDrYEZmgLjlBXMg9AAMBB/GrqJPz26EHgBgFoQegAWqPYxe93qWERJ6ALbxoFKYJqEHYAnhB6ZF6AG4AMGHMdGReTmhB2APBB8YP6EHYI8EHzbeKh8oeqFlhIQegH3QzwfGS+gBOADBh01V59azjJHQA3BAgg+MywUfOAoAjMhI+9usg0oPwCGo9sB4qPQAHNL54PPqF7z4mFsC451DZx1UegBWxMgu2GxCD8CKCT4cm84oHjhaVZdW1f1V9ejw95Ilx52tqgeH5d6F7ddU1UeH97+nqi7ey3mFHoAjIPjArt6c5APdfW2SDwzrO/mD7r5uWF6zsP3tSd4xvP8LSd6wl5MKPQBHRPDhOIzk2Vs3JblreH1Xktfu+fqqKsnLk9yz3/cLPQBHSPCBHT2/u59IkuHv85Yc96yqOlVVH6mq88HmOUm+2N1PD+unk1yxl5MavQVwxE6eecjILtZnfaO3LquqUwvrd3T3HedXqur9Sb5xh/f98D7O8U3dfaaqviXJB6vqE0l+d4fj9nTVQg8AcBCf6+4Ty3Z29yuX7auqz1bV5d39RFVdnuTJJZ9xZvj7eFV9OMlLkvx8kmdX1TOGas+VSc7spcFubwGswfnh7G53QZLk3iS3Dq9vTfK+7QdU1SVV9czh9WVJXprkU93dST6U5HW7vX8nQg/Amgk+HJXKaDoy357khqp6NMkNw3qq6kRV/dRwzAuTnKqqh7IVcm7v7k8N+96U5Ieq6rFs9fF5115O6vYWwDHQz4c56+7PJ3nFDttPJfn+4fWvJPm2Je9/PMn1+z2vSg/AMVHxYeXWNTHhIScnPC5CD8AxEnxgfdzeAjhmHljKKnng6HIqPQAbQtUHjpZKD8AGUfXh0FR6llLpAQBmQegB2EBudXFQI5mn51gIPQAbSvCB1dKnB2CD6ePDvnSScyMtw6yBSg/ACKj6wOEJPQAjIfiwJ72mZYSEHoAREXzg4PTpARgZ/XzYzVhHVq2DSg/ASJ0885DKD+yD0AMwcoIP7I3bWwAwJe3+1jIqPQAToNoDFyb0AEyE4EPiMRS7EXoAJkTwgeX06QGYmMXgY1j7zIx44sB1UOkBmDCVH/gTQg/AxAk+81FJqnstyxgJPQAzIPiA0AMwG4LPTJxb0zJCQg8AMAtCD8CMqPZMnz49ywk9ADPjQaXMldADMFOCzwT1GpcREnoAZkzVhzkRegAQfCajt56yvo5lhIQeAJIIPkyfZ28B8MfOBx/P7BqvsT4BfR1UegD4Kqo+TJHQA8COBB+mxu0tAJiSkXYyXgeVHgCWUu1hSlR6ANiVzs0j0kmN9GGg66DSA8CemMiQsRN6ANgXwWfDmZxwKaEHgH0TfBgjoQeAAxF8NpQHji4l9ABwYIIPY2L0FgCHYnTXZqmR9rdZB5UeAGAWVHoAWAkVnw2h0rOUSg8AK6WfD5tK6AFg5QSfY9JJzq1pGSGhB4AjIfiwafTpAeDI6OezXpU2emsXKj0AHDlVHzaB0APAWgg+HDe3twBYG7e71sDtraVUegBYO1UfjoNKDwBMiUrPUio9ABwL1R7WTaUHgGOjj8+KnZ+ckB2p9ABw7FR9WAehB4CNIPisRnWvZRkjoQeAjSH4cJSEHgA2iuBzSN3rWQ6hqi6tqvur6tHh7yU7HPNdVfXgwvKHVfXaYd/PVNVvLuy7bi/n1ZEZgI2zGHx0cp6kNyf5QHffXlVvHtbftHhAd38oyXXJVkhK8liSf7lwyN/q7nv2c1KVHgA2msrPfqypynP4Pj03JblreH1Xktde4PjXJfkX3f37hzmp0AMArNvzu/uJJBn+Pu8Cx9+c5N3btr2tqj5eVe+oqmfu5aRCDwAbT7VnjzrrrPRcVlWnFpbbFptSVe+vqk9vWBtTAAAJK0lEQVTusNy0n0uqqsuTfFuSkwub35LkW5N8R5JLs+3W2DL69AAwCifPPKR/z2b5XHefWLazu1+5bF9VfbaqLu/uJ4ZQ8+Qu5/neJL/Y3f/fwmc/Mbz8clX9dJK/uZcGq/QAMBoqPntwbk3L4dyb5Nbh9a1J3rfLsbdk262tISilqipb/YE+uZeTCj0AjMrJMw8JP+N3e5IbqurRJDcM66mqE1X1U+cPqqqrk1yV5P/c9v6fq6pPJPlEksuS/PheTur2FgCj5Lld49Xdn0/yih22n0ry/Qvrv5Xkih2Oe/lBzqvSA8Coqfp8JY+hWE7oAWD0BB/2QugBYBIEn8E4Jic8FkIPADALOjIDMBmz79zcSc6NswqzDio9AEyOW13sROgBYJLmGXxG88DRYyH0ADBZJjJkkdADwOTNKvio9Cwl9AAwC7MKPuzoUKGnqm6sqk9X1WNV9eZVNQoAjsIsbnep9Cx14NBTVRcleWeS707yoiS3VNWLVtUwADgqkw8+7OgwlZ7rkzzW3Y939x8luTvJTatpFgAcrUkGn/Pz9KxjGaHDhJ4rknxmYf10dngSKgDAJjhM6Kkdtn1V9Kuq26rqVFWd+p3Pnz3E6QBgtaZX7emkz61nGaHDPIbidJKrFtavTHJm+0HdfUeSO5LkxIkT/TXfeOoQpwSA1br/CP/7XbVTfYDjcphKz8eSXFtV11TVxUluTnLvapoFALBaB670dPfTVfXGJCeTXJTkzu5+eGUtAwD2b6TDydfhUE9Z7+77kty3orYAAByZQ4UeAGCDnB+yzo48hgIAmAWVHgCYEn16llLpAQBmQaUHAKZEpWcplR4AYBZUegBgMlqlZxcqPQDALKj0AMBUdJJz43wY6Dqo9AAAs6DSAwBTok/PUio9AMAsqPQAwJSo9Cyl0gMAzILQAwDMgttbADAZnZxze2sZlR4AYBZUegBgKjrpNjnhMio9AMAsqPQAwJTo07OUSg8AMAsqPQAwJSYnXEqlBwCYBZUeAJiK7uSc0VvLqPQAALOg0gMAU6JPz1IqPQDALKj0AMCEtD49S6n0AACzoNIDAJPR+vTsQqUHAJgFoQcAmAW3twBgKjoeOLoLlR4AYBZUegBgStqQ9WVUegCAWVDpAYCJ6CStT89SKj0AwCyo9ADAVHTr07MLlR4AYBaEHgCYkD7Xa1kOo6peX1UPV9W5qjqxy3E3VtWnq+qxqnrzwvZrquqjVfVoVb2nqi7ey3mFHgBg3T6Z5D9N8svLDqiqi5K8M8l3J3lRkluq6kXD7rcneUd3X5vkC0nesJeTCj0AMCV9bj3LYZrY/Uh3f/oCh12f5LHufry7/yjJ3UluqqpK8vIk9wzH3ZXktXs5r9ADAGyiK5J8ZmH99LDtOUm+2N1Pb9t+QWsdvfXAAw98qaoulOzG7LIknzvuRhwh1zdurm+8pnxtybSv75vXebLfyxdOvr/vuWxNp3tWVZ1aWL+ju+84v1JV70/yjTu874e7+317+PzaYVvvsv2C1j1k/dPdvbTD0thV1SnXN16ub9ymfH1TvrZk+te3Tt1943G34bzufuUhP+J0kqsW1q9MciZbAfnZVfWModpzfvsFub0FAGyijyW5dhipdXGSm5Pc292d5ENJXjccd2uSvVSOhB4AYL2q6i9X1ekk/2GSf15VJ4ftL6iq+5JkqOK8McnJJI8keW93Pzx8xJuS/FBVPZatPj7v2st51317644LHzJqrm/cXN+4Tfn6pnxtyfSvj226+xeT/OIO288k+Z6F9fuS3LfDcY9na3TXvtRWlQgAYNrc3gIAZmEtoWfZNNJTUVW/VVWfqKoHtw3fG62qurOqnqyqTy5su7Sq7h+m/b6/qi45zjYe1JJr+7Gq+n+H3/DBqvqe3T5jk1XVVVX1oap6ZJjm/QeH7VP5/ZZd3yR+w6p6VlX9alU9NFzf3x62H2ja/U2zy/X9TFX95sLvd91xt5XpOfLbW8M00v8myQ3ZGn72sSS3dPenjvTEa1RVv5XkRHdPZp6JqvqLSb6U5Ge7+88N2/5ukqe6+/YhvF7S3W86znYexJJr+7EkX+ru/+k427YKVXV5ksu7+9eq6s8keSBbs5V+X6bx+y27vu/NBH7DYbbZr+vuL1XV1yb5V0l+MMkPJfmF7r67qv5Bkoe6+yePs60Hscv1/fUkv9Td9+z6AXAI66j07DiN9BrOyyF09y8neWrb5puyNd13so9pvzfNkmubjO5+ort/bXj9e9ka9XBFpvP7Lbu+SegtXxpWv3ZYOgecdn/T7HJ9cOTWEXqWTSM9JZ3kX1bVA1V123E35gg9v7ufSLb+w5PkecfcnlV7Y1V9fLj9NcpbP9tV1dVJXpLko5ng77ft+pKJ/IZVdVFVPZjkyST3J/mNHHDa/U20/fq6+/zv97bh93tHVT3zGJvIRK0j9Bx4uugReWl3//lsPQn2B4bbJ4zLTyb5d5Ncl+SJJP/z8Tbn8Krq65P8fJK/0d2/e9ztWbUdrm8yv2F3n+3u67I10+z1SV6402HrbdXqbL++qvpzSd6S5FuTfEeSS7M1Dwus1DpCz7JppCdjmFcg3f1ktuYd2PfcASPx2aE/xfl+FU8ec3tWprs/O/xDfC7JP8rIf8Ohr8TPJ/m57v6FYfNkfr+drm9qv2GSdPcXk3w4yXdmmHZ/2DWJf0cXru/G4bZld/eXk/x0JvD7sXnWEXp2nEZ6Deddi6r6uqEzZarq65K8Ksknd3/XaN2brem+k31M+z0G58PA4C9nxL/h0FH0XUke6e6/v7BrEr/fsuubym9YVc+tqmcPr/9Ukldmq9/Sgabd3zRLru//Xgjkla3+SqP8/dhsa5mccBg6+hNJLkpyZ3e/7chPuiZV9S35k1kln5Hkf5/C9VXVu5O8LFtPP/5skh9N8s+SvDfJNyX57SSv7+7RdQhecm0vy9ZtkU7yW0n+q/P9X8amqv6jJP9Xkk8kOTds/h+y1e9lCr/fsuu7JRP4Davq27PVUfmibP2P6Xu7+63DvzV3Z+vWz68n+StDVWRUdrm+DyZ5bra6RDyY5K8vdHiGlTAjMwAwC2ZkBgBmQegBAGZB6AEAZkHoAQBmQegBAGZB6AEAZkHoAQBmQegBAGbh/weK3N5JuFC4kQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f_approach_sector_side(x, y):    \n",
    "    to_faf_x = x_faf - x\n",
    "    to_faf_y = y_faf - y\n",
    "    \n",
    "    angle_faf = np.degrees(np.arctan2(to_faf_x, to_faf_y))\n",
    "    \n",
    "    approach_sector_side = np.sign(relative_angle(phi_runway, angle_faf))\n",
    "    \n",
    "    return approach_sector_side\n",
    "\n",
    "x_faf = 20\n",
    "y_faf = 15\n",
    "\n",
    "phi_runway = 310\n",
    "x_runway = 20\n",
    "y_runway = 20\n",
    "\n",
    "x = np.arange(0, 40, 0.1)\n",
    "y = np.arange(0, 40, 0.1)\n",
    "xx, yy = np.meshgrid(x, y, sparse=True)\n",
    "z = f_approach_sector_side(xx, yy)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.pcolormesh(x,y,z)\n",
    "plt.colorbar()\n",
    "ax = plt.gca()\n",
    "ax.set_aspect('equal', 'datalim')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-40"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relative_angle(phi_runway, 270)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f_reward_angle(x):\n",
    "    return np.power(-np.power((x-22.5)/202, 2)+1, 32)\n",
    "\n",
    "x = np.arange(-180, 180, 1)\n",
    "y = f_reward_angle(x)\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f_reward_on_intercept_course(x, y, phi_plane):    \n",
    "    to_faf_x = x_faf - x\n",
    "    to_faf_y = y_faf - y\n",
    "    d_faf = np.hypot(to_faf_x, to_faf_y)\n",
    "    \n",
    "    reward_faf = 1/np.maximum(np.power(d_faf, 0.6),1)\n",
    "    \n",
    "    angle_faf = np.degrees(np.arctan2(to_faf_y, to_faf_x))\n",
    "    reward_app_sector = np.power(np.abs(relative_angle(phi_runway, angle_faf))/180, 1.5)\n",
    "    \n",
    "    plane_to_runway = relative_angle(phi_runway, phi_plane)\n",
    "    side = f_approach_sector_side(x, y)\n",
    "    \n",
    "    reward = f_reward_angle(side * plane_to_runway) * reward_app_sector * reward_faf\n",
    "    \n",
    "    return reward\n",
    "\n",
    "x_faf = 20\n",
    "y_faf = 15\n",
    "\n",
    "phi_runway = 310\n",
    "phi_plane = 280\n",
    "\n",
    "x_runway = 20\n",
    "y_runway = 20\n",
    "\n",
    "x = np.arange(0, 40, 0.1)\n",
    "y = np.arange(0, 40, 0.1)\n",
    "xx, yy = np.meshgrid(x, y, sparse=True)\n",
    "z = f_reward_on_intercept_course(xx, yy, phi_plane)\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.pcolormesh(x,y,z, vmin=0.0, vmax=1.0)\n",
    "plt.colorbar()\n",
    "ax = plt.gca()\n",
    "ax.set_aspect('equal', 'datalim')\n",
    "plt.title(\"Angle based reward for phi_runway=%d and phi_plane=%d\" % (phi_runway, phi_plane))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "49806b1095d741f9bc9395f6c6e62c0e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=180.0, description='phi_plane', max=360.0), Output(layout=Layout(heigh…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import interactive\n",
    "\n",
    "x = np.arange(0, 40, 0.5)\n",
    "y = np.arange(0, 40, 0.5)\n",
    "xx, yy = np.meshgrid(x, y, sparse=True)\n",
    "\n",
    "def plot_interactive_approach_sector_reward(phi_plane):\n",
    "    z = f_reward_on_intercept_course(xx, yy, phi_plane)\n",
    "    \n",
    "    plt.figure(figsize=(10,10))\n",
    "    plt.pcolormesh(x,y,z, vmin=0.0, vmax=1.0)\n",
    "    plt.colorbar()\n",
    "    ax = plt.gca()\n",
    "    ax.set_aspect('equal', 'datalim')\n",
    "    plt.title(\"Angle based reward for phi_runway=%d and phi_plane=%d\" % (phi_runway, phi_plane))\n",
    "    plt.show()\n",
    "\n",
    "interactive_plot = interactive(plot_interactive_approach_sector_reward, phi_plane=(0.0, 360.0))\n",
    "output = interactive_plot.children[-1]\n",
    "output.layout.height = '650px'\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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